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The fundamental function of certain interpolation spaces generated by $$N$$-tuples of rearrangement-invariant spaces. (English) Zbl 1393.46014
Jain, Pankaj (ed.) et al., Function spaces and inequalities, New Delhi, India, December 11–15, 2015. Singapore: Springer (ISBN 978-981-10-6118-9/hbk; 978-981-10-6119-6/ebook). Springer Proceedings in Mathematics & Statistics 206, 1-14 (2017).
Summary: In this paper we determine the fundamental function of the space obtained by applying an exact interpolation functor of exponent $$\overline{\theta}$$ to an $$N$$-tuple of rearrangement-invariant function spaces. Results apply to the extension of the real method studied by A. Yoshikawa [J. Fac. Sci., Univ. Tokyo, Sect. I 16, 407–468 (1970; Zbl 0197.09901)] and G. Sparr [Ann. Mat. Pura Appl., IV. Ser. 99, 247–316 (1974; Zbl 0282.46022)], and to the extension of the complex method investigated by J.-L. Lions [C. R. Acad. Sci., Paris 251, 1853–1855 (1960; Zbl 0118.10702)] and A. Favini [Rend. Sem. Mat. Univ. Padova 47, 243–298 (1972; Zbl 0248.46032)]. Moreover, we also consider the case of the general real method for couples of spaces.
For the entire collection see [Zbl 1382.46004].

MSC:
 46B70 Interpolation between normed linear spaces 46E30 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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